How localized bosons manage to become superfluid

We show that the many-body wavefunction built as a permanent of localized non-orthogonal single-particle states can describe bosonic superfluidity. The criterion for the transition is expressed in terms of the properties of the matrix of the overlaps between the single-particle wavefunctions. We apply this result to study the superfluid-to-Bose glass transition in a disordered Bose-Hubbard model through a very simple variational wavefunction. We finally consider a further quantity, the bipartite entanglement entropy, which also provides a good estimator for the superfluid-to-Bose glass transition.